One to one function

Question

G= (-5,5), (-1,8), (5,9), (9,0), hx=3x-8 find what g^-1(9)= and what (h^-1×h)(2)=

Answer 1

So keep in mind about the inverse function we know f(x)=y where x is the input or x-values and y is the output or y-values. The inverse function it flips the x and y to f^-1(y)=x

With that being said its asking for g^-1(9) = x and that 9 represents a y-value so can you find what x is?

with (h^-1°h)(2) this implies h^-1(h(2)) = x

Find the inverse of this function you can follow these procedure

We know h(x) = y so we can rewrite h(x) = 3x-8 to y = 3x-8

Step 1) we flip the x and y

y = 3x-8 switch the x and y and turns into this x = 3y-8

Step 2) solve for y

y= x/3 + 8/3 this is our inverse of h(x)

h^-1(y) = y/3 +8/3 or you can rewrite as h^-1(x) = x/3 +8/3

h^-1(h(2)) = h^-1(3(2)-8) = h^-1(-2) = -2/3 + 8/3 = 6/3 = 2

so (h^-1°h)(2) = 2

Hope this help feel free to ask any questions.

Answer 2

1) The third ordered pair in G is (5,9) which implies that G(5)=9 and hence, G^(-1)(9) = 5.

2) h(x) = 3x-8. Step 1 would be to find inverse of this function.

y=3x-8

y+8 = 3x

(y+8)/3 = x

Therefore, h^(-1) (x) = (x+8)/3

h(2) = 3*2 - 8 = 6-8 = -2

h^(-1) (h(2)) = h^(-1) (-2)

= (-2+8)/3

= 2

Note: A general result h^(-1) (h(a)) = a