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The function h(x) = –x5 12x is an odd function. which transformation of h(x) results in an odd function? h(5 – x) 1 h(x) h(x 8) –6h(x)

Respuesta :

The transformation of the odd function h(x) = [tex](-x)^{5}+12x[/tex], which is also an odd function is 1+h(x).

What is odd function?

  • A function f(x) is said to be odd, if for all x = -x, f(-x) = -f(x).

Given: [tex]h(x)=(-x)^{5} +12x[/tex] is an odd function.

Then, h(-x) = - h(x) as it is an odd function,

That is, LHS = h(-x) [tex](-(-x))^{5} +12(-x) = x^{5}-12x = - ( (-x)^{5} + 12x)[/tex] = RHS

Now, for [tex]h'(x) = 1+h(x) = 1+(-x)^{5} + 12(x)[/tex] ,

(where, h'(x) = transformation of h(x)),

  • If h'(x) is an odd function, then 1 + h(-x) = 1 - h(x)

=>LHS = [tex]1+h(-x)=1+(-(-x))^{5}-12(-x)=1+x^{5}+12x[/tex]

And, [tex]1-h(x)=1-((-x)^{5}-12x)=1+x^{5}+12x[/tex]

As 1 + h(-x) = 1 - h(x), the transformation h'(x) = 1 + h(x) is an odd function.

To learn more about odd function from the given link:

https://brainly.com/question/2284364

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