Question

If f(x) = 3x + 5 and g(x) = $x^3$ – 7, then find fog(x).

• A. -132 + 225x - 135$x^2$ + 27$x^3$
• B. 3$x^3$ + 16
• C. 132 + 225x + 135$x^2$ + 27$x^3$
• D. 3$x^3$ - 16

Answer 1

Answer: (D)

3$x^3$ - 16

Answer 2

To find $fog(x)$, we need to substitute the function $g(x)$ into the function $f(x)$. This means wherever 'x' appears in $f(x)$, we replace it with the entire expression for $g(x)$.

Given: $f(x) = 3x + 5$ $g(x) = x^3 - 7$

We need to find $fog(x)$, which is defined as $f(g(x))$.

Substitute $g(x)$ into $f(x)$: $f(g(x)) = f(x^3 - 7)$

Now, replace 'x' in the expression for $f(x)$ with $(x^3 - 7)$: $f(x^3 - 7) = 3(x^3 - 7) + 5$

Expand and simplify the expression: $3(x^3 - 7) + 5 = 3x^3 - 3 \times 7 + 5$ $= 3x^3 - 21 + 5$ $= 3x^3 - 16$

Therefore, $fog(x) = 3x^3 - 16$.