Question

which of the following represents the function ( f(g(h(x))) ) if ( f(x) = 10x ), ( g(x) = \frac{2x}{5} ), and ( h(x) = x^2 )?

a. ( \frac{x}{4} )

b. ( 4x^2 )

c. ( \frac{2x}{3} )

d. ( \frac{2x^2}{7} )

Explanation:

Step1: Compute $g(h(x))$

Substitute $h(x)=x^3$ into $g(z)=\frac{2z}{5}$:
$g(h(x))=\frac{2x^3}{5}$

Step2: Compute $f(g(h(x)))$

Substitute $g(h(x))=\frac{2x^3}{5}$ into $f(z)=10z$:
$f(g(h(x)))=10\times\frac{2x^3}{5}$

Step3: Simplify the expression

Calculate the product and cancel terms:
$10\times\frac{2x^3}{5}=\frac{20x^3}{5}=4x^3$

Answer:

B. $4x^3$