Question

If $f(x)=3x-2$ and $g(x)=\frac{1}{3}x+1$, then $(f(g))^{-1} (x)$ equals:

a. $1-x$
b. $x-1$
c. $\frac{1}{3} (3x-1)$
d. $x+1$

Answer 1

Answer:

• B) x - 1

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Given

• f(x) = 3x - 2, g(x) = 1/3x + 1

Find the composite function f(g(x))

• f(g(x)) = 3(1/3x +1) - 2 = x + 3 - 2 = x + 1

Find the inverse of f(g(x))

• x = f(g)⁻¹(x) + 1
• f(g)⁻¹(x) = x - 1

Correct choice is B