Question

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Given that f(x) = x2 − 3x + 3 and g(x) = the quantity of x minus one, over four, solve for f(g(x)) when x = 5.

−3

1

7

13

Answer 1

Plug in g(x) into f( )

\(f(\color{red}{x})= \color{red}{x}^2-3\color{red}{x}+3\), So the idea will be to substitute g(x) wherever you see "x" in your function:


\(f(\color{red}{g(x)}) =(\color{red}{g(x)})^2-3\color{red}{g(x)}+3 \)
\[ f\left(\color{red}{\frac{x-1}{4} }\right)=\left(\color{red}{\frac{x-1}{4} }\right)^2-3\left(\color{red}{\frac{x-1}{4} }\right)+3\]

Answer 2

Then all you need to do is substitute the value of x=5 in the last expression above^

Answer 3

is it 1 ?

Answer 4

yes indeed