2021-12-28

Suppose the rule of the function f is "add one" and the rule of the function g is "multiply by 4."
How can we express these functions algebraically?
$f\left(x\right)=$
$g\left(x\right)=$
$\left(f\circ g\right)\left(x\right)=$
$\left(f\circ g\right)\left(x\right)=$

Ella Williams

Expert

Given:
Suppose the rule of the function f is "add one" and the rule of the function g is "multiply by 4".
Calculation:
To express the function algebraically:
Here, f and g are function of x.
From the given information,
$f\left(x\right)=x+1$
$g\left(x\right)=4x$
$\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$
$=f\left(4x\right)$
$\left(f\circ g\right)\left(x\right)=4x+1$, (using $f\left(x\right)=x+1$)
$\left(g\circ f\right)\left(x\right)=g\left(f\left(x\right)\right)$
$=g\left(x+1\right)$
$=4\left(x+1\right)$, (using $g\left(x\right)=4x\right)$
$\left(g\circ f\right)\left(x\right)=4x+4$

Cassandra Ramirez

Expert

We have to find the algebraically function f and g where f is "add one" and g is "multiply by 4"
Solution: $f\left(\in put\right)=\in put+1$
$⇒f\left(x\right)=x+1$
and $g\left(x\right)=4x$
$\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)=f\left(4x\right)=4x+1$
$\left(f\circ g\right)\left(x\right)=g\left(f\left(x\right)\right)=g\left(x+1\right)=4\left(x+1\right)$
$\left(f\circ g\right)\left(x\right)=4x+4$

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