Question

If f(x) = 3x + 5 and g(x) = x² -7, then find fog(x).

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

Answer 1

Answer: (D)

$3x^2-16$

Answer 2

To find fog(x), we need to substitute the function g(x) into f(x).

Given functions: $f(x) = 3x + 5$ $g(x) = x^2 - 7$

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

Step 1: Replace 'x' in the expression for f(x) with the entire expression for g(x). $f(g(x)) = f(x^2 - 7)$

Step 2: Substitute $(x^2 - 7)$ into the formula for $f(x)$. $f(x) = 3x + 5$ So, $f(x^2 - 7) = 3(x^2 - 7) + 5$

Step 3: Distribute the 3 into the parenthesis. $3(x^2 - 7) + 5 = 3x^2 - 3 \times 7 + 5$ $= 3x^2 - 21 + 5$

Step 4: Combine the constant terms. $3x^2 - 21 + 5 = 3x^2 - 16$

Thus, $fog(x) = 3x^2 - 16$.

The problem asks for the composite function $fog(x)$, which means $f(g(x))$. We are given $f(x) = 3x + 5$ and $g(x) = x^2 - 7$. To find $f(g(x))$, we substitute the expression for $g(x)$ into $f(x)$ in place of $x$. So, $f(g(x)) = f(x^2 - 7)$. Now, using the definition of $f(x)$, we replace $x$ with $(x^2 - 7)$: $f(x^2 - 7) = 3(x^2 - 7) + 5$. Distributing the 3, we get $3x^2 - 21 + 5$. Combining the constant terms, we obtain $3x^2 - 16$.