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.