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3 years ago

Help me pleaseeeeeeeee

Mathematics

1 answer:

SIZIF [17.4K]3 years ago

4 0

Answer:

(f o g)(x) = 4x^4 - 24x^2 + 37

(g o f)(x) = 16x^4 + 8x^2 - 2

Step-by-step explanation:

f(x) = 4x^2 + 1

g(x) = x^2 - 3

(f o g)(x) = f(g(x)) = f(x^2 - 3) = 4(x^2 - 3)^2 + 1 =

= 4(x^4 - 6x^2 + 9) + 1

= 4x^4 - 24x^2 + 37

(g o f)(x) = g(f(x)) = g(4x^2 + 1) = (4x^2 + 1)^2 - 3 =

= 16x^4 + 8x^2 - 2

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If f(x)= 3-2 and g(x)=1/x+5 what is the vue of (f/g) (8)

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Answer:

The value of (f/g) (8) = -169

Step-by-step explanation:

<u>Step 1: explaining the question</u>

The quotient (f/g) is not defined at values of x ⇒ both the functions must be defined at a point for the combination to be defined.

⇒(f/g)(x) =(f(x)) / (g(x))

If f(x)= 3-2 and g(x)=1/x+5

⇒then according to the preceding formula: (f/g)(x) =(f(x)) / (g(x))

⇒(f/g)(8) = f(8) / g(8)

to solve this we have to find the value of both f(8) and g(8)

<u>Step 2: find value of f(8) and g(8)</u>

⇒ we know that f(x) = 3-2x and we know dat f(x) = f(8)

⇒ f(8) = 3-2(8)

f(8) = 3-16 = -13

⇒we know that g(x) = 1/x+5 and g(x) = g(8)

⇒ g(8) = 1/8+5

g(8) =1/13

These 2 equations we will insert in the following : ⇒(f/g)(8) = f(8) / g(8)

⇒ f/g (8) = -13 / (1/13) = -13 * 13/1 = -169

The value of (f/g) (8) = -169

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