Answered

Can someone please help me with problem number 8? The answer is below the problem. This is algebra 2 by the way. Directions: Given f(x) = 2x^2-9x+2, g(x) = 1 - 6x, and h(x) = x^2 - 4, find the function. Indicate any restrictions in the domain. ​

Can someone please help me with problem number 8 The answer is below the problem This is algebra 2 by the way Directions Given fx 2x29x2 gx 1 6x and hx x2 4 fin class=


Answer :

msm555

Answer:

[tex](h \circ f)(x) = 4x^4 - 36x^3 + 89x^2 - 36x[/tex]

Step-by-step explanation:

The notation [tex](h \circ f)(x)[/tex] represents the composition of functions [tex]h[/tex] and [tex]f[/tex], denoted as [tex]h(f(x))[/tex]. To find [tex](h \circ f)(x)[/tex], we substitute [tex]f(x)[/tex] into the function [tex]h(x)[/tex].

Given:

  • [tex] f(x) = 2x^2 - 9x + 2 [/tex]
  • [tex] h(x) = x^2 - 4 [/tex]

To find [tex](h \circ f)(x)[/tex], substitute [tex]f(x)[/tex] into [tex]h(x)[/tex]:

[tex] (h \circ f)(x) = h(f(x)) [/tex]

[tex] (h \circ f)(x) = h(2x^2 - 9x + 2) [/tex]

Now, substitute [tex]2x^2 - 9x + 2[/tex] into [tex]h(x)[/tex]:

[tex] (h \circ f)(x) = (2x^2 - 9x + 2)^2 - 4 [/tex]

Now, expand and simplify:

[tex] (h \circ f)(x) = (2x^2 - 9x + 2)(2x^2 - 9x + 2) - 4 [/tex]

Multiply the terms:

[tex] (h \circ f)(x) = (2x^2 )(2x^2 - 9x + 2) -9x(2x^2 - 9x + 2) +2(2x^2 - 9x + 2)- 4 [/tex]

[tex] (h \circ f)(x) = 4x^4 - 18x^3 +4x^2 - 18x^3 + 81x^2 - 18x + 4x^2 - 18x + 4 - 4 [/tex]

Combine like terms:

[tex] (h \circ f)(x) = 4x^4 - 36x^3 + 89x^2 -36x[/tex]

So, [tex](h \circ f)(x) = 4x^4 - 36x^3 + 89x^2 - 36x[/tex].