F⁻¹(x) is the notation for the inverse of an equation, so you just need to find the inverse equation. that's found by swapping your x and y variables:
<span>f(x) = 2x + 2 ... replace f(x) with y
y = 2x + 2 ... swap x and y variables
x = 2y + 2 ... solve for y
x = 2y + 2 ... subtract 2
x - 2 = 2y ... divide by 2
(x - 2)/2 = y
so, </span>f⁻¹(x) = (x - 2)/2 ... now you need to solve that for when x = 4. plug it in:
f⁻¹(x) = (4 - 2)/2 ... simplify the top of the fraction
f⁻¹(x) = 2/2
f⁻¹(x) = 1 is your answer.
I would but my teacher has a ad blocker on and I cant access the attachment :P
That's all the square roots of the form 5.xxxx. The numbers start at 5² and end at 6²-1.
So that's 6² - 5² = 11 numbers. We can list them:
25,26,27,28,29,30,31,32,33,34,35
Answer: 11
X +5 = -6x - 16
add 16 to both sides
x+21 = -6x
add 6x to both sides
7x+21=0
factor out the seven
7(x+3)=0
if 7 times (x+3) = 0 then (x+3) must equal zero because 7 times 0 is 0
so x+3=0
subtract three from both sides
x= -3
