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marishachu [46]
2 years ago
12

For f(x) =1/x^2-3 find: (a) f(3) (3 points) (b) f(2+h) (3 points)

Mathematics
1 answer:
siniylev [52]2 years ago
3 0

Answer:

f(3) = \frac{-26}{9}

f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}

Step-by-step explanation:

Given

f(x) = \frac{1}{x^2} - 3

Required

Find f(3) and f(2 + h)

Solving f(3)

Substitute 3 for x in f(x) = \frac{1}{x^2} - 3

f(3) = \frac{1}{3^2} - 3

f(3) = \frac{1}{9} - 3

Take LCM

f(3) = \frac{1 - 27}{9}

f(3) = \frac{-26}{9}

Solving f(2 + h)

Substitute 2 + h for x in f(x) = \frac{1}{x^2} - 3

f(2 + h) = \frac{1}{(2 + h)^2} - 3

f(2 + h) = \frac{1}{(2 + h)(2 + h)} - 3

f(2 + h) = \frac{1}{4 + 2h + 2h + h^2} - 3

f(2 + h) = \frac{1}{4 + 4h + h^2} - 3

Take LCM

f(2 + h) = \frac{1- 3(4 + 4h + h^2)}{4 + 4h + h^2}

f(2 + h) = \frac{1- 12 - 12h - 12^2}{4 + 4h + h^2}

f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}

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