The table below shows some inputs and outputs of the invertible function fff with domain all real numbers.
xxx 141414 -6−6minus, 6 -1−1minus, 1 101010 -10−10minus, 10 333
f(x)f(x)f, left parenthesis, x, right parenthesis 777 -10−10minus, 10 -15−15minus, 15 141414 -4−4minus, 4 -9−9minus, 9
Find the following values:
f^{-1}(f^{-1}(7))=f
−1
(f
−1
(7))=f, start superscript, minus, 1, end superscript, left parenthesis, f, start superscript, minus, 1, end superscript, left parenthesis, 7, right parenthesis, right parenthesis, equals
7
f^{-1}(-4)=f
−1
(−4)=f, start superscript, minus, 1, end superscript, left parenthesis, minus, 4, right parenthesis, equals
(thats for the people who copied and pasted it off Khan Academy.)

PS: I DONT KNOW IF IT IS CORRECT!!!!! please, someone check it.

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MrRoyal MrRoyal · Answer 1 · 2022-06-13T22:11:04+02:00

The value of f⁻¹(f⁻¹(7)) is 10

The expression is given as:

f⁻¹(f⁻¹(7))

We start by solving the inner expression f⁻¹(7).

The above means that we determine the x value when y = 7.

So, we have:

f⁻¹(7) = 14

Substitute f⁻¹(7) = 14 in f⁻¹(f⁻¹(7))

f⁻¹(14)

Next, we determine the x value when y = 14

f⁻¹(14) = 10

Hence, the value of f⁻¹(f⁻¹(7)) is 10