Question

Represent the function f(x)=✓2x² - 5x +3 as a composition of two functions.​

Answer 1

$\huge\bold\color{aqua}{Answer:–}$

The standard form of the

quadratic function

is.

y

=

a

x

2

+

b

x

+

c

To factorise the function.

• consider the factors of the product ac which sum to give b

for

2

x

2

+

5

x

−

3

a

=

2

,

b

=

5

and

c

=

−

3

⇒

a

c

=

2

×

−

3

=

−

6

the required factors of -6 are

+

6

and

−

1

since

6

×

−

1

=

−

6

and

+

6

−

1

=

+

5

now express

2

x

2

+

5

x

−

3

as

2

x

2

+

6

x

−

x

−

3

Factorise by 'grouping'

⇒

2

x

(

x

+

3

)

−

1

(

x

+

3

)

Take out

common factor

of

(

x

+

3

)

⇒

(

x

+

3

)

(

2

x

−

1

)

←

in factorised form