English

Answer the following: If f(x) = 3x + a and f(1) = 7 find a and f(4) - Mathematics and Statistics

Advertisements
Advertisements

Question

Answer the following:

If f(x) = 3x + a and f(1) = 7 find a and f(4)

Sum

Solution

f(x) = 3x + a 

∴ f(1) = 3(1) + a = 3 + a

∴ f(1) = 7 gives

3 + a = 7

∴ a = 4

∴ f(x) = 3x + 4

∴ f(4) = 3(4) + 4 = 16.

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Functions - Miscellaneous Exercise 6.2 [Page 130]

APPEARS IN

RELATED QUESTIONS

Let f be the subset of Z × Z defined by f = {(ab, a + b): a, b ∈ Z}. Is f a function from Z to Z: justify your answer.


Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine

(b) {x : f(x) = −2}


If f(x) = x2, find \[\frac{f\left( 1 . 1 \right) - f\left( 1 \right)}{\left( 1 . 1 \right) - 1}\]


Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function: 

(v) \[\frac{g}{f}\]

 

Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function: 

(viii) \[\frac{5}{8}\]

 

If fg and h are real functions defined by 

\[f\left( x \right) = \sqrt{x + 1}, g\left( x \right) = \frac{1}{x}\] and h(x) = 2x2 − 3, find the values of (2f + g − h) (1) and (2f + g − h) (0).
 
 

Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (g) (x), (f − g) (x), (fg) (x) and  \[\left( \frac{f}{g} \right) \left( x \right)\] .

 

Write the range of the function f(x) = cos [x], where \[\frac{- \pi}{2} < x < \frac{\pi}{2}\] .

 

If\[f\left( x \right) = 1 - \frac{1}{x}\] , then write the value of \[f\left( f\left( \frac{1}{x} \right) \right)\]

 

 


Write the domain and range of function f(x) given by

\[f\left( x \right) = \frac{1}{\sqrt{x - \left| x \right|}}\] .
 

If f(x) = cos (log x), then value of \[f\left( x \right) f\left( 4 \right) - \frac{1}{2} \left\{ f\left( \frac{x}{4} \right) + f\left( 4x \right) \right\}\] is 


If  \[f\left( x \right) = \frac{2^x + 2^{- x}}{2}\] , then f(x + yf(x − y) is equal to

 


If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g(f(x)) = 8 are


The domain of the function \[f\left( x \right) = \sqrt{\frac{\left( x + 1 \right) \left( x - 3 \right)}{x - 2}}\] is

  

The domain of definition of  \[f\left( x \right) = \sqrt{4x - x^2}\] is 

 

The range of the function \[f\left( x \right) = \frac{x + 2}{\left| x + 2 \right|}\],x ≠ −2 is

 

The range of  \[f\left( x \right) = \frac{1}{1 - 2\cos x}\] is 

 


If f(m) = m2 − 3m + 1, find f(0)


Show that if f : A → B and g : B → C are one-one, then g ° f is also one-one


Express the following logarithmic equation in exponential form

log2 64 = 6


Express the following logarithmic equation in exponential form

`log_5  1/25` = – 2


Write the following expression as a single logarithm.

ln (x + 2) + ln (x − 2) − 3 ln (x + 5)


Answer the following:

A function f is defined as : f(x) = 5 – x for 0 ≤ x ≤ 4. Find the value of x such that f(x) = 5


Answer the following:

Let f : R → R be given by f(x) = x3 + 1 for all x ∈ R. Draw its graph


Answer the following:

Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0


Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - 3) + 1/(log(5 - x))`


A function f is defined by f(x) = 2x – 3 find x such that f(x) = x


The range of 7, 11, 16, 27, 31, 33, 42, 49 is ______.


The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.


Mapping f: R → R which is defined as f(x) = sin x, x ∈ R will be ______ 


Let f : R → R be defined by 

f(x) = `{(3x;    x > 2),(2x^2;    1 ≤ x ≤ 2), (4x;   x < 1):}`

Then f(-2) + f(1) + f(3) is ______ 


If f(x) = `{{:(x^2",", x ≥ 0),(x^3",", x < 0):}`, then f(x) is ______.


Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.


The domain of the function f defined by f(x) = `1/sqrt(x - |x|)` is ______.


Find the range of the following functions given by f(x) = 1 – |x – 2| 


Redefine the function f(x) = x − 2 + 2 + x , – 3 ≤ x ≤ 3


Find the domain and range of the function f(x) = `1/sqrt(x - 5)`


If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.


Range of f(x) = `1/(1 - 2 cosx)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×