Advertisements
Advertisements
Question
If f(x) = 3x + 5, g(x) = 6x − 1, then find (fg) (3)
Solution
f(x) = 3x + 5, g(x) = 6x – 1
(fg) (3) = f(3) g(3)
= [3 (3) + 5] [6 (3) – 1]
= (14) (17)
= 238
APPEARS IN
RELATED QUESTIONS
What is the fundamental difference between a relation and a function? Is every relation a function?
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(c) whether f(xy) = f(x) : f(y) holds
f, g, h are three function defined from R to R as follow:
(iii) h(x) = x2 + 1
Find the range of function.
The function f is defined by \[f\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 3 \\ 3x, & 3 \leq x \leq 10\end{cases}\]
The relation g is defined by \[g\left( x \right) = \begin{cases}x^2 , & 0 \leq x \leq 2 \\ 3x, & 2 \leq x \leq 10\end{cases}\]
Show that f is a function and g is not a function.
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
If f(x) = (a − xn)1/n, a > 0 and n ∈ N, then prove that f(f(x)) = x for all x.
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:
(ii) 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:
(iii) f g
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
Find the set of values of x for which the functions f(x) = 3x2 − 1 and g(x) = 3 + x are equal.
If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to
If \[f\left( x \right) = \log \left( \frac{1 + x}{1 - x} \right) \text{ and} g\left( x \right) = \frac{3x + x^3}{1 + 3 x^2}\] , then f(g(x)) is equal to
If 2f (x) − \[3f\left( \frac{1}{x} \right) = x^2\] (x ≠ 0), then f(2) 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
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(0)
Express the following exponential equation in logarithmic form
`9^(3/2)` = 27
Express the following logarithmic equation in exponential form
`log_5 1/25` = – 2
Express the following logarithmic equation in exponential form
`log_(1/2) (8)` = – 3
If x = loga bc, y = logb ca, z = logc ab then prove that `1/(1 + x) + 1/(1 + y) + 1/(1 + z)` = 1
Answer the following:
Identify the following relation is the function? If it is a function determine its domain and range.
{(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
Answer the following:
If b2 = ac. prove that, log a + log c = 2 log b
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Answer the following:
Find the range of the following function.
f(x) = 1 + 2x + 4x
Given the function f: x → x2 – 5x + 6, evaluate f(2)
A function f is defined by f(x) = 2x – 3 find x such that f(x) = x
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) = `3/(2 - x^2)`
Domain of `sqrt(a^2 - x^2) (a > 0)` is ______.
The domain of the function f defined by f(x) = `sqrt(4 - x) + 1/sqrt(x^2 - 1)` is equal to ______.
The domain and range of real function f defined by f(x) = `sqrt(x - 1)` is given by ______.
Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.