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- If f ( x ) = x² + 2x - 1 and g ( x ) = 3x - 2 , then verify the following :
1. [tex] \large{ \bf{( \frac{f}{g})(2) = \frac{f(2)}{g(2)} }}[/tex]
- Irrelevant / Random answers will be reported! *​

Respuesta :

Sueraiuka

Step-by-step explanation:

Hey there!

Given;

f ( x ) = x² + 2x - 1

g ( x ) = 3x - 2

To verify:

[tex]( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} [/tex]

LHS:

[tex] (\frac{f}{g} )(x) = \frac{ {x}^{2} + 2x - 1}{3x - 2} [/tex]

~ Insert "2" instead of "x".

[tex] (\frac{f}{g} )(2) = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} [/tex]

Simplify it;

[tex] \frac{f}{g} (2) = \frac{4 + 4 - 1}{6 - 2} [/tex]

Therefore; (f/g)(2) = 7/4.

RHS:

[tex] \frac{f(x)}{g(x)} = \frac{ {x}^{2} + 2x - 1}{3x - 2} [/tex]

~Insert "2" instead of"x".

[tex] \frac{f(2)}{g(2)} = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} [/tex]

Simplify it.

[tex] \frac{f(2)}{g(2)} = \frac{4 + 4 - 1}{6 - 2} [/tex]

Therefore, f(2)/g(2) = 7/4.

Since (f/g)(2) = f(2)/g(2) = 7/4.

Proved!

Hope it helps!

HayabusaBrainly

Step-by-step explanation:

  • f(x) = x² + 2x - 1
  • g(x) = 3x - 2

Soo :

[tex] \tt( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} [/tex]

[tex] \tt( \frac{ {x}^{2} + 2x - 1 }{3x - 2} )(2) = \frac{ {2}^{2} + 2(2) - 1 }{3(2) - 2} [/tex]

[tex] \tt( \frac{ {2}^{2} + 2(2) - 1}{3(2) - 2} )= \frac{7}{4} [/tex]

[tex] \boxed{ \tt \frac{7}{4} = \frac{7}{4} }[/tex]

Soo true.

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