Find g[f(5)] if f(x) = x + 1 and g(x) = 3x - 2.?

g (f (x)) = 3 (x + 1) - 2 = 3x + 3 - 2 = 3x + 1

<=>

g (f (5)) = 3 (5) + 1 = 15 + 1 = 16

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g ( f ( x ) ) = g ( x + 1 ) = 3 x + 1

g ( f ( 5 ) ) = 16

f(x) = x + 1
g(x) = 3x - 2

g(x) → g[f(x)] = g(x + 1)

g(x + 1) = 3(x + 1) - 2
g(x + 1) = 3x + 3 + 2
g(x + 1) = 3x + 5

g(x) → g[f(x)] → g[f(5)] = g(5 + 1)

g(5 + 1) = 3(5 + 1) - 2
g(6) = 3(6) - 2
g(6) = 18 - 2
g(6) = 16

g[f(5)]=3(x+1)-2
=3x+3-2
=3x+1
=3(5)+1
=15+1
=16 answer//

f(5)= 5+1=6

g(f(5)) = g(6) = 3x6 - 2 =18 - 2 = 16

f(x) = x + 1
Putting x = 5,

f(5) = 5 + 1 = 6


g(x) = 3x - 2

g[f(5)] = 3[f(5)] - 2
= 3(6) - 2
= 18 - 2
= 16

Hence, the ans. is 16

g ( f (x) )

= 3 * f(x) - 2

= 3 * (x + 1) - 2.

To find g(f(5)), just substitute x by 5.