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Evaluate inverse functions

Find the following values f^-1(f(3.14))
F(f(-7))

Evaluate Inverse Functions Find The Following Values F1f314 Ff7 class=

Sagot :

Answer:

1. 3.14

Step-by-step explanation:

If we have

[tex]f {}^{ - 1} (f(x)[/tex]

That just equals

[tex]x[/tex]

For example, consider function

[tex]f(x) = 2 {}^{x} [/tex]

The inverse of that function is

[tex]y = 2 {}^{x} [/tex]

[tex]x = 2 {}^{y} [/tex]

[tex] log_{2}(x) = log_{2}(2 {}^{y} ) [/tex]

[tex] log_{2}(x) = y[/tex]

So

[tex]f {}^{ - 1} (x) = log_{2}(x) [/tex]

If we compose the function, f(x) into f^-1(x).

We get

[tex] log_{2}(2 {}^{x}) = x[/tex]

That proof of that.

1. Here x=f^-1(3.14)and f(3.14) cancel out so the answer is 3.14

2. We first find f(-7) which is -12,

We then find f(-12)= 5 so the answer here is 5.

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