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Use function composition to verify f(x)=-3x+5 and g(x)=\frac{x-5}{-3} are inverses. When typing your answer if you have an exponent then use the carrot key ^ by pressing SHIFT and 6. Type your simplified answers in descending powers of x an do not include any spaces between your characters.Type your answer for this composition without simplifying:the numerator of g(f(x))=Answerthe denominator g(f(x))=AnswerNow simplify the composition, are f(x) and g(x) inverses? Answer

Use function composition to verify fx3x5 and gxfracx53 are inverses When typing your answer if you have an exponent then use the carrot key by pressing SHIFT an class=

Respuesta :

We are given the following functions:

[tex]\begin{gathered} f(x)=-3x+5 \\ g(x)=\frac{x-5}{-3} \end{gathered}[/tex]

We are asked to determine the composite function:

[tex]g(f(x))[/tex]

To do that we will replace as the value of "x" in g(x) the function f(x), like this:

[tex]g(f(x))=\frac{(-3x+5)-5}{-3}[/tex]

Therefore, the numerator of the composite function is:

[tex]\text{ numerator g(f(x))=-3x+5-5}[/tex]

And the denominator is:

[tex]\text{ denominator g(f(x))=-3}[/tex]

Now we simplify the fraction, first by canceling out the 5:

[tex]g(f(x))=\frac{-3x}{-3}[/tex]

Now we cancel out the -3:

[tex]g(f(x))=x[/tex]

Since the composite function is "x" this means that the functions are inverses of each other.

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