Problem 7: For 𝑓(𝑥) = 𝑥−3/ 𝑥+1 , a) Find the inverse function 𝑓 −1 (𝑥) b) Sketch f and f -1 on the same
axes. Check that they have symmetry across the line y = x
a) Find the inverse function 𝑓 −1 (𝑥)
we will change 𝑓(𝑥) to y  y=x-3/x+1
we will switch the position of the variables x and y  x=y-3/y+3
Put x over 1 and cross multiply x/1 = y-3/y+3  cross multiplication gives us xy+x=y-3
We then subtract xy and add 3 to the opposite side of the equation giving us x+3=-xy+y
We need to get y by itself in order to get the inverse, so our next step will need to be factoring
out the y from the right side of the equation giving us x+3=y(-x+1)
6) We divide both sides of the equation by -x+1 and we are left with the inverse of 𝑓(𝑥) = 𝑥−3/ 𝑥+1
ANS: 𝑓 −1 (𝑥)=x+3/-x+1
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b) Sketch f and f -1 on the same axes. Check that they have symmetry across the line y = x
Problem 8: Given f(x)=x^2, find the equation of a function h(x) after performing the following
transformations: Reflect across the x-axis, shift to the left by 3 units, then shift up by 4 units.
1) In order to create a reflection on the x-axis, we will add a negative sign to the outputs of the
function-(x)^2
2) Next we will shift the function left by 3 units-(x+3)^2
3) Finally we shift the function up by 4 units-(x+3)^2+4
4) Our transformed function is h(x)= -(x+3)^2+4