Question

93. Let f(x) = 3x - 1 and g(x) = x + 5. Evaluate the following limits. (a) lim x→3 f(g(x)]

(b) lim x→3 g[f(x)]

Answer 1

a) 23 and b) 13

Explanation:

I. If f(g(x)) is composit function

Find fog and gof

fog = 3(g) - 1

= 3(x+5) -1

= 3x + 15 -1

= 3x + 14

gof = (f) + 5

= (3x - 1) +5

= 3x + 4

II. Fill in a) and b) question

lim x -> 3 fog

= 3(x) + 14

= 3(3) + 14

= 9 + 14

a) = 23

lim x-> 3 gof

= 3x + 4

= 3(3) + 4

= 9 + 4

b) = 13

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