Question

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

• A. $3x^2+16$
• B. -132 + 225x - 135x² + 27x³
• C. 132 + 225x + 135x² + 27x³
• D. $3x^3-16$

Answer 1

$3x^2+16$

Answer 2

The given functions are $f(x) = 3x + 5$ and $g(x) = x^2 - 7$. The question asks to "find log(x)". This is highly likely a typographical error. In the context of functions $f(x)$ and $g(x)$ and given the options, it is almost certainly intended to be a question about function composition, specifically $f(g(x))$ (which means $f(g(x))$) or $g(f(x))$ (which means $g(f(x))$). This interpretation is strongly supported by the "similar question" provided, which asks for $f(g(x))$ with the exact same functions.

Let's calculate $f(g(x))$:

$f(g(x)) = f(g(x))$

Substitute the expression for $g(x)$ into $f(x)$:

$f(g(x)) = f(x^2 - 7)$

Now, replace $x$ in $f(x) = 3x + 5$ with $(x^2 - 7)$:

$f(x^2 - 7) = 3(x^2 - 7) + 5$

Distribute the 3:

$= 3x^2 - 3 \times 7 + 5$

$= 3x^2 - 21 + 5$

Combine the constant terms:

$= 3x^2 - 16$

So, if the question meant $f(g(x))$, the result is $3x^2 - 16$.

Our calculated result, $3x^2 - 16$, is not directly available in the options. However, option 1 is $3x^2+16$, which differs from our result only by the sign of the constant term. This is a common type of error in multiple-choice questions. Given that the exact answer $3x^2-16$ is not present, but a very close variant $3x^2+16$ is, it suggests a typo in the question or the options provided.

If we strictly interpret the question as "find log(x)", it is unanswerable based on the given $f(x)$ and $g(x)$. Given the context of function composition problems, we proceed with the assumption that "log(x)" is a typo for "f(g(x))".

Since $3x^2-16$ is not an option, and $3x^2+16$ is the closest option in form, it's possible that there's an intended sign change in the problem's constants or the option itself. For instance, if $f(x) = 3x-5$ and $g(x)=x^2+7$, then $f(g(x)) = 3(x^2+7)-5 = 3x^2+21-5 = 3x^2+16$. This would match option 1. However, this requires changing the given functions.

Given the strong resemblance to the similar question, the most probable scenario is a typo in the options. Assuming that one of the options must be correct, and that the question implicitly expects the closest answer, we choose $3x^2+16$.