Question

Given that f(x) = 4x − 3 and g(x) = quantity of 2x minus 1, divided by 3 solve for g(f(2)).

Answer 1

we have

$f(x)=4x-3$

$g(x)=(2x-1)/3$

Step $1$

Find the value of $f(2)$

calculate the value of f(x) for $x=2$

$f(2)=4*2-3$

$f(2)=5$

Step $2$

Find the value of $g(f(2))$

calculate the value of g(x) for $x=f(2)$

so

$x=5$

$g(5)=(2*5-1)/3$

$g(5)=3$

therefore

$g(f(2))=3$

the answer is

$3$

Answer 2

Value of g (f (2)) = 3

Further explanation

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y

A function can be expressed in the form of a cartesian diagram, sequential pairs, or arrow diagram

Like the number operations we do in real numbers, operations such as addition, subtraction, division or multiplication can also be done on two functions.

Suppose a function f (x) and g (x) then:

(f + g) (x) = f (x) + g (x)

(f + g) (x) is a new function of the sum of f (x) and g (x)

the other function operations:

• (f-g) (x) = f (x) - g (x)
• (fg) (x) = f (x) x g (x)
• (f / g) (x) = f (x) / g (x)

In addition to the above operations, we can combine two functions using the function composition with the symbol "o"

(fog) (x) = f (g (x))

(gof) (x) = g (f (x))

Given

$f(x)=4x-3$

$g(x) = \frac{2x-1}{3}$

Then g(f (2))

f(2) = 4.2 -3

f(2) = 5

g(f (x) = g (5)

$g(5)=\frac{2.5-1}{3}$

g(5) = 3

so g(f(2)) = 3

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Keywords: composition function