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g(x) = 4x+6
h(x)=x-5
Write the expressions for (g-h) (x) and (g-h) (x) and evaluate (g- h) (3).
(g-h)(x) =
(g-h)(x) = 0
(g+h)(3) =

Sagot :

jaytzy1234567

Answer:

(g-h)(x) = x+3-2x2

(g+h)(x) = x+ 3 +2x2

to evaluate, replace x by -3 and compute, carefully.

semsee45

Answer:

[tex](g-h)(x) = 3x+11[/tex]

[tex](g+h)(x) = 5x+1[/tex]

[tex](g-h)(3) =20[/tex]

[tex](g+h)(3) =16[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}g(x)=4x+6\\h(x)=x-5\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

Therefore, the composite function (g-h)(x) means subtract function h(x) from function g(x).  Similarly, (g+h)(x) means to add function h(x) to function g(x).

[tex]\begin{aligned}(g-h)(x) & = g(x)-h(x)\\& = (4x+6)-(x-5)\\& = 4x+6-x+5\\& = 4x-x+6+5\\& = 3x+11\end{aligned}[/tex]

[tex]\begin{aligned}(g+h)(x) & = g(x)+h(x)\\& = (4x+6)+(x-5)\\& = 4x+6+x-5\\& = 4x+x+6-5\\& = 5x+1\end{aligned}[/tex]

To evaluate both composite functions when x = 3, simply substitute x = 3 into the found composite functions:

[tex]\begin{aligned}(g-h)(3) & = 3(3)+11\\& = 9+11\\&=20\end{aligned}[/tex]

[tex]\begin{aligned}(g+h)(3) & = 5(3)+1\\& = 15+11\\&=16\end{aligned}[/tex]

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