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hjlf
1 year ago
11

Question 19 of 25 f(x)=√x-6. Find the inverse of f(x) and its domain.

Mathematics
1 answer:
Gekata [30.6K]1 year ago
5 0

Answer:

f¯¹(x)=x²+12x+36

Step-by-step explanation:

f(x) =  \sqrt{x}  - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y =  \sqrt{x}  - 6 \\ interchange \: x \: and \: y \\ x =  \sqrt{y}  - 6 \\ swap \: the \: side \: of \: the \: equation \\  \sqrt{y }  - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\   \sqrt{y}  = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2}  + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2}  + 12x + 36 \\ domain \: x∈R

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