Question

If function $f: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $f(x) = 2x - 3$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $g(x) = x^3 + 5$, then the value of $(f \circ g)^{-1}(-9)$ is:

• A. $-2$
• B. $-1$
• C. $0$
• D. $1$

Hint:

Work backwards from $h(x) = y$ to find inverse: solve the composed equation for $x$.

Answer 1

The Correct Option is A

Let $h(x) = f(g(x)) = f(x^3 + 5) = 2(x^3 + 5) - 3 = 2x^3 + 10 - 3 = 2x^3 + 7$
We want: $h(x) = -9 \Rightarrow 2x^3 + 7 = -9 \Rightarrow 2x^3 = -16 \Rightarrow x^3 = -8 \Rightarrow x = -2$