Think about the operations of a function that create its inverse. Without doing any work, explain in words why f(x)=1/2x+4 and g(x)=2x+8 are not inverses of each other.

Answer 1

Multiplication and division are inverse operations of each other. I see multiplication by 2 in one and division by 2 in the other, so those match up. However, both of them I see addition. In order for them to be inverses, I would expect to see addition in one and subtraction in the other.

Answer 2

f(x) add 4 and divides by 2

g(x) adds 8 and multiplies by 2

to be an inverse, the inverse operations are necessary

g(x) should subtract 8 and multiply by 2

f(x) = (1/2)x +4 = y

(1/2)y +4 = x

solve for y

(1/2)y = x-4

y = 2(x-4) = 2x-8

Answer 3

Inverse functions are symmetrical across the y=x line (the diagonal that cuts through the origin). One of these functions has a y-intercept of 4 and the other a y-intercept of 8, both above the origin so, since they are both straight lines, they could not possibly be symmetrical across the y=x line

Answer 4

f(x)=(x/2)+4

g(x)=2x+8

for all x in domain for f(x), have points (x,f(x))

if g(x) is inverse of f(x)

then g(x) will have corresponding points (f(x),x)

for f(x),,,x=2, f(2)=5 ,,,have point (2,5)

for g(x) x=5, g(5)=18,,have point (5,18),,,should be (5,2) if g were inverse of f