Which function is the inverse of function f?

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

=>

Replace y with g(x)

Option D is correct.

Option D

 for

Step-by-step explanation:

We have the following function

make

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

Now interchange the variable x with the variable y

 for

Finally, make g(x) = y

 for

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4