[tex]\boxed{ \ f(g(x)) = 31 - 40x\ }[/tex]
Further explanation
This is a question about the composition of functions. Composition of functions is when one function is inside of another function. If we are given two functions, it is possible to generate or produce a new function by arranging one to another.
The order in function composition is so important. We always compose functions from right to left. Therefore, its input is consistently the one to its right side. Put differently, the right function goes inside the left function.
Let's look at these:
- The g function is inside of the f function [tex]\boxed{ \ (f o g)(x) = f(g(x)) \ }[/tex]
- The f function is inside of the g function [tex]\boxed{ \ (g o f)(x) = f(g(x)) \ }[/tex]
Given [tex]f(x) = - 4x + 7 \ and \ g(x) = 10x - 6.[/tex]
Find [tex] f(g(x)) [/tex]
Replace each appearance of x in f(x) with [tex] g(x) = 10x - 6.[/tex] as input.
[tex]\boxed{ \ f(g(x)) = -4(10x - 6) + 7 \ }[/tex]
Simplify the proper answer by distributing and combining like terms. Multiply -4 into parentheses.
[tex]\boxed{ \ f(g(x)) = -40x + 24 + 7 \ }[/tex]
Thus, [tex]\boxed{ \ f(g(x)) = -40x + 31 \ or \ f(g(x)) = 31 - 40x\ }[/tex]
Extra question:
From the same problem, solve for [tex]f(g(-1)).[/tex]
Replace the variable x in f (g (x)) with -1.
[tex] \ f(g(-1)) = 31 - 40(-1) \ }[/tex]
[tex] \ f(g(-1)) = 31 + 40 \ }[/tex]
Hence, [tex]\boxed{ \ f(g(-1)) = 71 \ }[/tex]
Learn more
- If f(x) = x² – 2x and g(x) = 6x + 4, for which value of x does (f o g)(x) = 0? https://brainly.com/question/1774827
- Solve for the value of the function composition https://brainly.com/question/2142762
- Look for rotation rules in the transformation https://brainly.com/question/2992432
Keywords: composition of function, a new function, the value, the f function is inside of the g, produce, compose, right to left
