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3 years ago

Need help understanding this problem please

Mathematics

1 answer:

faust18 [17]3 years ago

7 0

f(g(x)) is a composite function:

$f(g(x))=f(\sqrt{x+5})=2\sqrt{x+5}-1$

Plug in <em>x</em> = 4:

$f(g(4)) = 2\sqrt{4+5}-1=2\sqrt9-1=2\cdot3-1=\boxed{5}$

so the answer is C.

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<u>Solution:</u>

Given, expression is $3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)$

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Now, take the given expression.

$\rightarrow 3 \log (x+4)-2 \log (x-7)+5 \log (x-2)-\log \left(x^{2}\right)$

Rearranging the terms we get,

$\left.\rightarrow 3 \log (x+4)+5 \log (x-2)-2 \log (x-7)+\log \left(x^{2}\right)\right)$

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$\text { We know that } \log a \times \log b=\log a b$

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