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Solve the following.
The values of two functions f and g for certain values of x are given in the following table: x -2…
The values of two functions $f$ and $g$ for certain values of $x$ are given in the following table:
| $x$ | -2 | 0 | 3 |
|---|---|---|---|
| $f(x)$ | -12 | -4 | 8 |
| $g(x)$ | 0 | -12 | 30 |
(a)[1]
Find the value of $f^{-1}(8)$?
(b)[1]
Given that $f(x)$ is a linear function, find $f(x)$?
Answer
Answer (a)
Official answer key$f(3) = 8$
$\therefore f^{-1}(8) = 3$
Final answer: 3
Answer (b)
Official answer keySince $f(x)$ is a linear function, the graph of $y = f(x)$ is a straight line.
$m = \frac{-4 + 12}{0 + 2} = \frac{8}{2} = 4$
$\therefore y = 4x + (-4)$ ($\because$ $y$-intercept $= -4$ from the table)
$y = 4x - 4$
$\therefore f(x) = 4x - 4$
Final answer: $4x - 4$