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Karo-lina-s [1.5K]
2 years ago
6

25 POINTS PLZ HELP ASAP!!! Match the functions with their inverse functions.

Mathematics
2 answers:
elena55 [62]2 years ago
8 0
<h2>Answer with explanation:</h2>

We know that when we are given a inverse function as: f^{-1}(x)

Then we find the function by the method:

Put f^{-1}(x)=y

Then we switch the places of x and y and solve for y.

1)

f^{-1}(x)=\dfrac{2x-3}{5}

Hence, we find the function as follows:

\dfrac{2x-3}{5}=y

Then we switch for x and y

\dfrac{2y-3}{5}=x\\\\\\i.e.\\\\2y-3=5x\\\\\\i.e.\\\\\\2y=5x+3\\\\\\i.e.\\\\\\y=\dfrac{5x+3}{2}

Hence, inverse function is:

  f(x)=\dfrac{5x+3}{2}

2)

f^{-1}(x)=\dfrac{x+8}{2}

Hence, we find the function as follows:

\dfrac{x+8}{2}=y

Then we switch for x and y

\dfrac{y+8}{2}=x

y=2x-8

Hence, inverse function is:

           f(x)=2x-8

3)

f^{-1}(x)=\dfrac{x+2}{7}

Hence, we find the function as follows:

\dfrac{x+2}{7}=y

Then we switch for x and y

\dfrac{y+2}{7}=x

y=7x-2

Hence, inverse function is:

           f(x)=7x-2

4)

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

Hence, we find the function as follows:

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

Then we switch for x and y

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

i.e.

1-2y=xy\\\\xy+2y=1\\\\i.e.\\\\y(x+2)=1\\\\y=\dfrac{1}{x+2}

Hence, inverse function is:

  f(x)=\dfrac{1}{x+2}

antoniya [11.8K]2 years ago
6 0
To calculate the inverse isolate x on one side and switch x with y on both sides

1)
y=(2x-3)/5
5y=2x-3
5y+3=2x
(5y+3)/2=x
-> f(x)=(5x+3)/2

2)
y=(x+8)/2
2y=x+8
2y-8=x
-> f(x)=2x-8

3)
y=(x+2)/7
7y=x+2
7y-2=x
-> f(x)=7x-2

4)
y=(1-2x)/x
y=(1/x)-2
y+2=1/x
x=1/(y+2)
-> f(x)=1/(x+2)
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\small{\underline{\tt{\red{Given}}}}

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