If f (x) = 4x - 3 and g (x) = 8x + 2, find each function value

a. f[g (3) ]

b. g[f (5) ]

c. g{f[g (-4) ]}

f[g (3) ] = 100

g[f (5) ] = 138

g{f[g (-4) ]} = - 982

Step-by-step explanation:

f (x) = 4x - 3

g (x) = 8x + 2

a. f[g (3) ]

First find g (3) by putting x = 3 in g (x) function

g (3) = 8 (3) + 2 = 24 + 2 = 26

now put this g (3) = 26 as x in f (x)

f (g (3)) = f (26) = 4 (26) - 4 = 104 - 4 = 100

b. g[f (5) ]

First lets find f (5)

f (x) = 4x - 3

put x = 5 above

f (5) = 4 (5) - 3 = 20 - 3 = 17

put this f (5) = 17 as x in g (x)

g (f (5)) = g (17) = 8 (17) + 2 = 138

c. g{f[g (-4) ]}

First lets solve the inner most function

g (-4) = 8 (-4) + 2 = - 30

put g (-4) = - 30 in f (x) to find f (g (-4))

f (g (-4)) = f (-30) = 4 (-30) - 3 = - 123

put f (g (-4)) = - 123 as x in g (x) to find our complete result

g{f[g (-4) ]} = g (-123) = 8 (-123) + 2 = - 982