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3 years ago

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1 answer:

hjlf3 years ago

3 0

Step-by-step explanation:

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Х- а<br>x-b<br>If f(x) = b.x-a÷b-a + a.x-b÷a - b<br>Prove that: f (a) + f(b) = f (a + b)

GenaCL600 [577]

Given:

Consider the given function:

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}$

To prove:

$f(a)+f(b)=f(a+b)$

Solution:

We have,

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}$

Substituting $x=a$ , we get

$f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}$

$f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}$

$f(a)=0+a$

$f(a)=a$

Substituting $x=b$ , we get

$f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}$

$f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}$

$f(b)=b+0$

$f(b)=b$

Substituting $x=a+b$ , we get

$f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}$

$f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}$

$f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}$

$f(a+b)=\dfrac{b^2-a^2}{b-a}$

Using the algebraic formula, we get

$f(a+b)=\dfrac{(b-a)(b+a)}{b-a}$ $[\because b^2-a^2=(b-a)(b+a)]$

$f(a+b)=b+a$

$f(a+b)=a+b$ [Commutative property of addition]

Now,

$LHS=f(a)+f(b)$

$LHS=a+b$

$LHS=f(a+b)$

$LHS=RHS$

Hence proved.

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3 years ago

Select all angles that are coterminal with an angle of rotation of 300 degrees

geniusboy [140]

The answers would be A,B,D, and F!

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4 years ago

Read 2 more answers

How many solutions does this system of equations have?

8_murik_8 [283]

No solutions

if you substitute the equations into each other the x's and y's will cancel each other out and you will be left with 9=-6 which isn't true<span />

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3 years ago

Katarina tosses a thumbtack on the ground 20 times to see if it lands on its side or if it lands with the point

Nesterboy [21]

Answer:

ajajajajaja

Step-by-step explanation:ahahaha

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3 years ago

Alicia cashed her paycheck and used half her earnings to take three friends out to dinner. She spent $42.15 and she brought home

Phoenix [80]

If you would like to write an inequality to represent the situation, using X to represent the amount of Alicia's paycheck, you can calculate this using the following steps:

X ... the amount of Alicia's paycheck

X/2 - $42.15 >= $20
X/2 >= $20 + $42.15
X/2 >= $62.15 /*2
X >= $62.15 * 2
X >= $124.3

The correct result would be <span>X >= $124.3</span>.

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3 years ago