Question

Given the definitions of f(x) and g(a) below, find the value of (f og)(-4).

f(x) = 3x2 – 5x – 4
g(x) = -4x – 12

Answer 1

✏️ FUNCTIONS

`\purple{\underline {\bold{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}`

`\bold \purple{PROBLEM:}`

» Given the definitions of f(x) and g(a) below, find the value of (f • g)(-4).

• f(x) = 3x2 – 5x – 4
• g(x) = -4x – 12

`\bold \purple{FORMULA:}`

`\underline{ \boxed{ \rm{ \green{(f \: • \: g)( - 4) }}}}`

`\bold \purple{SOLUTION:}`

Substitute the value of x into the given value which is -4. Lets simplify it.

`» \: \rm{(f \: • \: g)(-4) = [3 {x}^(2) – 5x – 4] \: • \: [-4x – 12]}`

`» \: \rm{(f \: • \: g)( \green{-4}) = [3 {( \green{ - 4})}^(2) – 5( \green{ - 4}) – 4 ]\: • \: [-4( \green{- 4})– 12]}`

`» \: \rm{(f \: • \: g)( \green{-4}) =[ 3( \green {16}) – ( \green{ - 20}) – 4 ]\: • \:[ ( \green{16})– 12]}`

`» \: \rm{(f \: • \: g)( \green{-4}) = [ \green {48}– ( \green{ - 20}) – 4 ]\: • \:[ ( \green{4})]}`

`» \: \rm{(f \: • \: g)( \green{-4}) =[ \green{ 64}] \: • \: [( \green{4})]}`

`» \: \rm{(f \: • \: g)( \green{-4}) = \underline{\boxed{\green{256}}}}`

`\bold \purple{ANSWER:}`

`» \: \rm{(f \: • \: g)( \green{-4}) = \underline{\boxed{\green{256}}}}`

• Hence, the answer is 256.

`\purple{\underline {\bold{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}`

＼(^.^＼)

Answer 2

To solve for (fog)-4)

Replace x in the g(x) equation with -4 and solve, then replace x in f(x) with the solution and solve for final answer.

G(x) = -4(-4) -12 = 16 -12 = 4

F(x) = 3(4)^2 -5(4) -4 = 48 -20 -4 = 24

The answer is 24