Question

If f(x) =$\frac{1}{x}$, g(x) = $x^2$ and h(x) =$x^3$ find f[g(hf(x))].

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

f[g(hf(x))] is of the form f(y) where y = g(h(f(x))). To find this we should know what is h(f(x)). For that we will need f(x). when we get a function which is composite like this, we first evaluate the inner most function and feed it to the next function f(x) =$\frac{1}{x}$ This is the input for h(x).

h(f(x)) = h($\frac{1}{x}$)= $(\frac{1}{x}{)}^3$=$\frac{1}{x^3}$

g(h(f(x))) = g($\frac{1}{x^3}$)= $(\frac{1}{x^3}{)}^2$=$\frac{1}{x^6}$

f(g(h(f(x))))=f( $\frac{1}{x^6}$) = $\frac{1}{\left(\frac{1}{x^6}\right)}$= $x^6$