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andrew11 [14]
2 years ago
12

PLEASE HELP ASAP are f(x)=4/x-2-1 and g(x)=3/x+2-2 inverses of each other?​

Mathematics
1 answer:
GREYUIT [131]2 years ago
4 0

Answer:

To find the inverse of:

f (x)=\dfrac{4}{x-2}-1

Set the function to y:

\implies y=\dfrac{4}{x-2}-1

Rearrange to make x the subject:

\implies y+1=\dfrac{4}{x-2}

\implies (y+1)(x-2)=4

\implies xy-2y+x-2=4

\implies xy+x=2y+6

\implies x(y+1)=2y+6

\implies x=\dfrac{2y+6}{y+1}

Swap x and y:

\implies y=\dfrac{2x+6}{x+1}

Change y to the inverse of the function sign:

\implies f\:^{-1}(x)=\dfrac{2x+6}{x+1}

Rewrite g(x) as a fraction:

g(x)=\dfrac{3}{x+2}-2

\implies g(x)=\dfrac{3}{x+2}-\dfrac{2(x+2)}{x+2}

\implies g(x)=\dfrac{3-2(x+2)}{x+2}

\implies g(x)=\dfrac{3-2x-4}{x+2}

\implies g(x)=-\dfrac{2x+1}{x+2}

Therefore, as the inverse of f(x) ≠ g(x), the functions are NOT inverses of each other

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