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juin [17]
3 years ago
7

Which function is the inverse of function f?

Mathematics
2 answers:
Scorpion4ik [409]3 years ago
5 0

Answer:

Option D is correct.

Step-by-step explanation:

f(x)= 9x^2 -12

Let y = 9x^2 - 12

Switch places of x and y and solve for y

x = 9y^2 - 12

Adding 12 on both sides

x + 12 = 9y^2

Dividing both sides by 9

x+12/9 = y^2

=> Taking square root on both sides

=> \sqrt{y^2}= \sqrt{\frac{x+12}{9}}\\y=\pm\frac{\sqrt{x+12}}{3}

Replace y with g(x)

g(x)=\pm\frac{\sqrt{x+12}}{3}

Option D is correct.

lys-0071 [83]3 years ago
5 0

Answer: Option D

g(x)=\±\frac{\sqrt{x+12}}{3}  for x\geq -12

Step-by-step explanation:

We have the following function

f(x) = 9x^2-12

make f (x) = y

y = 9x^2-12

To find the inverse of the function, solve for the variable x

y+12 = 9x^2

x^2=\frac{y+12}{9}

x=\±\sqrt{\frac{y+12}{9}}

x=\±\frac{\sqrt{y+12}}{3}

Now interchange the variable x with the variable y

y=\±\frac{\sqrt{x+12}}{3}  for x\geq -12

Finally, make g(x) = y

g(x)=\±\frac{\sqrt{x+12}}{3}  for x\geq -12

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