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If f and g are real functions defined by $f (x) = x^2 + 7$ and $g (x) = 3x + 5$ , find each of the following
(a) $f (3) + g (- 5)$

(b) $f(1/2) \times g(14)$

(c) $f (- 2) + g (- 1)$

(d) $f (t) - f (- 2)$

(e) $(f(t) - f(5))/ (t - 5), if \: \: t \neq 5$

Answers (1)

Given data: $f(x) = x^2 + 7$ & $g(x) = 3x + 5$

$f(3) + g(-5) = [(3)^2 + 7] + [3(-5) + 5]$

$= 16 - 10$

$= 6$

$f( 1/2 ) \times g(14) = [(1/2)^2 + 7] \times [3 \times 14 + 5]$

$= 29/4 \times 47$

$= 1363/4$

$f(-2) + g(-1) = [(-2)^2 + 7] + [(-1) + 5]$

$= 11 + 2 = 13$

$f(t) - f(-2) = (t^2 + 7) - [(-2)^2 + 7]$

$= t^2 - 4$

$f(t) - f(5)/ t - 5$ , (t is not equal to 5) = $(t^2 + 7) - (5^2 + 7)/ t - 5$

$=( t^2 + 7 - 32)/t - 5$

$= (t^2 - 25)/ (t - 5)$

$=(t - 5) (t + 5)/(t - 5)$

$= t + 5$

Posted by

infoexpert21

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