Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given the definitions of f(x) and g(x) below, find the value of (g@f)(4). {:[f(x)=2x^(2)-2x-15],[g(x)=3x-4]:} Answer:

Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of (g∘f)(4) (g \circ f)(4) .\newlinef(x)=2x2−2x−15g(x)=3x−4 \begin{array}{l} f(x)=2 x^{2}-2 x-15 \\ g(x)=3 x-4 \end{array} \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Divide numbers written in scientific notationright chevron icon

Full solution

Q. Given the definitions of f(x) f(x) and g(x) g(x) below, find the value of (g∘f)(4) (g \circ f)(4) .\newlinef(x)=2x2−2x−15g(x)=3x−4 \begin{array}{l} f(x)=2 x^{2}-2 x-15 \\ g(x)=3 x-4 \end{array} \newlineAnswer:
  1. Find f(4)f(4): First, we need to find the value of f(4)f(4) by substituting xx with 44 in the function f(x)f(x).\newlinef(4)=2(4)2−2(4)−15f(4) = 2(4)^2 - 2(4) - 15
  2. Calculate f(4)f(4): Now, let's perform the calculations for f(4)f(4).
    f(4)=2(16)−8−15f(4) = 2(16) - 8 - 15
    f(4)=32−8−15f(4) = 32 - 8 - 15
    f(4)=24−15f(4) = 24 - 15
    f(4)=9f(4) = 9
  3. Find g(f(4))g(f(4)): Next, we need to find the value of g(f(4))g(f(4)) by substituting f(4)f(4) into g(x)g(x). Since we found f(4)=9f(4) = 9, we will substitute xx with 99 in the function g(x)g(x). g(9)=3(9)−4g(9) = 3(9) - 4
  4. Calculate g(9)g(9): Now, let's perform the calculations for g(9)g(9).
    g(9)=3(9)−4g(9) = 3(9) - 4
    g(9)=27−4g(9) = 27 - 4
    g(9)=23g(9) = 23
  5. Final Answer: We have found the value of g(f(4))g(f(4)), which is g(9)=23g(9) = 23.\newlineThis is the final answer.

More problems from Divide numbers written in scientific notation

Question
Factor 16a+72 16 a+72 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 4(4a+18) 4(4 a+18) \newlineB 8(2a+9) 8(2 a+9) \newlineC 2(8+36a) 2(8+36 a) \newlineD 2(8a+72) 2(8 a+72)
Get tutor helpright-arrow

Posted 10 months ago

Question
Factor 30−6v−18w 30-6 v-18 w to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 2(15−12v) 2(15-12 v) \newlineB 3(10−3v+6w) 3(10-3 v+6 w) \newlinec 6(5−v−3w) 6(5-v-3 w) \newlineD 2(15−3v−9w) 2(15-3 v-9 w)
Get tutor helpright-arrow

Posted 10 months ago

Question
Factor 24m−12p+72 24 m-12 p+72 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 6(4m+2p+12) 6(4 m+2 p+12) \newlineB 2(12m−6p+36) 2(12 m-6 p+36) \newlinec 12(2m−p+6) 12(2 m-p+6) \newlineD 24(m−12p+3) 24(m-12 p+3)
Get tutor helpright-arrow

Posted 10 months ago

Question
Factor 48−8x 48-8 x to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 3(16−8x) 3(16-8 x) \newlineB 2(24−4x) 2(24-4 x) \newlinec 8(6−x) 8(6-x) \newlineD 4(12−4x) 4(12-4 x)
Get tutor helpright-arrow

Posted 7 months ago

Question
Multiply and simplify the following complex numbers:\newline(−3−2i)⋅(−4+2i) (-3-2 i) \cdot(-4+2 i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(1−2i)⋅(4+i) (1-2 i) \cdot(4+i)
Get tutor helpright-arrow

Posted 9 months ago

Question
Multiply and simplify the following complex numbers:\newline(−1+4i)⋅(4−3i) (-1+4 i) \cdot(4-3 i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(−4−4i)⋅(−5−3i) (-4-4 i) \cdot(-5-3 i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(1+5i)⋅(−3−i) (1+5 i) \cdot(-3-i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(−2+2i)⋅(5+5i) (-2+2 i) \cdot(5+5 i)
Get tutor helpright-arrow

Posted 10 months ago

View all (25)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant