
(a)
To Find :
How the graphs of f(x) and g(x) would appear on a coordinate grid.
(a)

Answer to Problem 15STP
If f(x) and g(x) are inverse functions , the points (x,y) and (y,x) will be symmetric along the line y = x .
Explanation of Solution
Given :
f(x) and g(x) are inverse functions.
Calculation:
Let f(x) = x+1Find its inverse, replace f(x) by 'y':y=x+1Interchange x and y:x=y+1Solve for y:y+1-1=x-1...............[subtract 1 from each side]y=x−1So, the inverse of the function f(x) = x+1 is g(x)=x−1Represent both the functions on the graph and also graph the equation y=x
Graph :
So, we observe that if f(x) and g(x) are inverse functions , the points (x,y) and (y,x) will be symmetric along the line y = x .
(b)
To Find :
The value of the composition f[g(2)]
(b)

Answer to Problem 15STP
f[g(2)]=2
Explanation of Solution
Given :
f(x) and g(x) are inverse functions.
Calculation:
We know that if f and g are inverse functions , then:[f∘g](x)=x[g∘f](x)=xSo,f[g(2)]=2 Since the input is 2 , apply g and then the inverse f reverses the changes applied by g on 2, hence the left output is 2.For example, from step (a)f(x)=x+1g(x)=x-1f[g(2)]=f(2-1)=f(1)=1+1=2
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