Question

Asiandoll

Use the functions h(x) = 2x − 5 and t(x) = 6x + 4 to complete the function operations listed below.

Part A: Find (h + t)(x). Show your work. (3 points)

Part B: Find (h ⋅ t)(x). Show your work. (3 points)

Part C: Find h[t(x)]. Show your work

Answer 1

Given h(x) = 2x- 5 and t(x) = 6x + 4

PART(A)

h(x) + t(x) is simply the sum of two functions so let's add the expression given for hx and tx

h(x) + t(x) = 2x -5 + 6x + 4

= 8x -1 Answer

PART (B)

( h. t)(x) is simply the product of two functions :

(2x-5)( 6x+4) = 2x* 6x + 2x*4 -5* 6x -5*4

= 12x^2 + 8x -30x -20

= 12x^2 -22x -20 Answer

PART (C)

When it is h( tx) it is composite function where tx is the inner function in the function hx

we rewrite the function hx by replacing x in it with tx = 6x+4

h (x)= 2x - 5

on left side x is replaced with t(x) and on right side we replace x with 6x+4

h( tx)= 2( 6x +4) - 5

h(tx) = 12 x + 2*4 - 5

h( tx) + 12x + 8 - 5

h( tx) = 12x + 3

Answer 12x +3