contestada

Suppose that ()=ℎ−1() j ( x ) = h − 1 ( x ) and that both j and ℎ h are defined for all values of x . Let ℎ(8)=4 h ( 8 ) = 4 and (9)=−1 j ( 9 ) = − 1 . Evaluate if possible and enter the value of the expression in the blank. If you do not have enough given information to evaluate the expression, enter unknown in the blank beside the expression.

H^-1(-1)=
J(H(8))=
H(J(8))=
J(4)=
J(8)=
J^-1(-1)=
H(9)=

Respuesta :

MrRoyal

When functions are combined to form a new function, the new function is called a composite function. The results of the expressions are:

  • [tex]h^{-1}(-1) = unknown[/tex].
  • [tex]j(h(8))= 8[/tex].
  • [tex]h(j(8)) = unknown[/tex].
  • [tex]j(4) = 8[/tex].
  • [tex]j(8) = unknown[/tex].
  • [tex]j^{-1}(-1) = 9[/tex].
  • [tex]h(9) = unknown[/tex]

Given that

[tex]j(x) = h^{-1}(x)[/tex]

[tex]h(8) = 4[/tex]

[tex]j(9) = -1[/tex]

[tex](a)\ h^{-1}(-1)[/tex]

Using [tex]j(x) = h^{-1}(x)[/tex]

The equation becomes

[tex]h^{-1}(-1) = j(-1)[/tex]

There is no sufficient information to calculate [tex]j(-1)[/tex]

So:

[tex]h^{-1}(-1) = unknown[/tex]

[tex](b)\ j(h(8))[/tex]

[tex]j(x) = h^{-1}(x)[/tex] means that:

[tex]j(h(x))= x[/tex]

So, we have:

[tex]j(h(8))= 8[/tex]

[tex](c)\ h(j(8))[/tex]

There is no sufficient to calculate j(8).

So:

[tex]h(j(8)) = unknown[/tex]

[tex](d)\ j(4)[/tex]

We have:

[tex]h(8) = 4[/tex]

This means that:

[tex]j(4) = 8[/tex]

[tex](e)\ j(8)[/tex]

There is no sufficient to calculate j(8).

So:

[tex]j(8) = unknown[/tex]

[tex](f)\ j^{-1}(-1)[/tex]

We have:

[tex]j(9) = -1[/tex]

This means that:

[tex]j^{-1}(-1) = 9[/tex]

[tex](g)\ h(9)[/tex]

There is no sufficient to calculate h(9).

So:

[tex]h(9) = unknown[/tex]

Read more about composite functions at:

https://brainly.com/question/20030485