3. INVERSES ALGEBRAICALLY: Given the function f(x) = 5( x+5 ) - 9, how is it represented in f⁻¹?

Answer 1

f(x) = 5(x + 25) - 9

f(x) = 5x + 25 - 9

f(x) = 5x + 16

x = 5f^-1(x) + 16

x - 16 = 5f^-1(x)

(x - 16) / 5 = f^-1(x)

Answer 2

f(x)=5(x+5)-9

y=5(x+5)-9

To find inverse, we start by replacing x with y and y with x. This gives us x=5(y+5)-9.

Now we solve for y. So first we'll distribute the 5, giving us x=5y+25-9.

Now combine the 25 and 9, giving us x=5y+16.

Now move the 5y to the left by subtracting 5y from each side of the equation. This gives us x-5y=16.

Next, we move the x to the right side by subtracting x from each side, giving us -5y=-x+16.

Finally, we divide by -5, giving us y=x/5-16/5.

So the inverse is f^-1(x)=x/5-16/5.