Question

f^-1(6) if f(x)=1/2^x+5​

Answer 1

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Here take y=f(x)

Then y=2x−6

⇒2x=y+6

⇒x=2y+3

Now switch x and y in the resulting equation. The resulting function of x is the inverse.

⇒y=2x+3

Thus the inverse function is f−1(x)=2x+3.

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Answer 2

Answer:

$f(x) = \frac{1}{2 {}^{x + 5} } . \\ f(6) = \frac{1}{2 {}^{6 + 5} } . \\ = \frac{1}{2 {}^{11} } = 2 {}^{11} .$