Advertisements
Advertisements
Question
If f(x) = ax2 + bx + 2 and f(1) = 3, f(4) = 42, find a and b.
Solution
f(x) = ax2 + bx + 2
f(1) = 3
∴ a(1)2 + b(1) + 2 = 3
∴ a + b = 1 …(i)
∴ f(4) = 42
∴ a(4)2 + b(4) + 2 = 42
∴ 16a + 4b = 40
Dividing by 4, we get
4a + b = 10 …(ii)
Solving (i) and (ii), we get
a = 3, b = – 2
APPEARS IN
RELATED QUESTIONS
If \[y = f\left( x \right) = \frac{ax - b}{bx - a}\] , show that x = f(y).
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
If f, g and h are real functions defined by
If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is
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 range of the function \[f\left( x \right) = \frac{x}{\left| x \right|}\] is
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Express the following exponential equation in logarithmic form
25 = 32
Express the following exponential equation in logarithmic form
3–4 = `1/81`
The equation logx2 16 + log2x 64 = 3 has,
Answer the following:
Without using log tables, prove that `2/5 < log_10 3 < 1/2`
Answer the following:
Show that, logy x3 . logz y4 . logx z5 = 60
The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.
| Length ‘x’ of forehand (in cm) |
Height 'y' (in inches) |
| 35 | 56 |
| 45 | 65 |
| 50 | 69.5 |
| 55 | 74 |
Find a and b
Domain of function f(x) = cos–1 6x is ______.
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 ______
Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`
The domain of f(x) = `sin^-1 [log_2(x/2)]` is ______.
