Question

1. evaluate the following, if a = 2, b = 4, c = 7

\\(\frac{a^{2}+b^{2}}{a - b}\\)

1. evaluate the following, if x=-4, y = 2

\\(-y^{2}-3xy\\)
example 3: evaluating functions in function notation

1. if f(x)=4x - 1, find f(-7)
2. if g(x)=2x^{2}-x, find g(-2)
3. find f(-4) y = f(x)
4. find f(9) y = f(x)

Explanation:

1. For the function $f(x)=4x - 1$, find $f(-7)$

Step1: Substitute $x=-7$

Substitute $x = - 7$ into $f(x)=4x - 1$. So we get $f(-7)=4\times(-7)-1$.

Step2: Calculate the result

$f(-7)=-28 - 1=-29$.

Step1: Substitute $x = - 2$

Substitute $x=-2$ into $g(x)=2x^{2}-x$. Then $g(-2)=2\times(-2)^{2}-(-2)$.

Step2: Calculate powers first

$(-2)^{2}=4$, so $g(-2)=2\times4 + 2$.

Step3: Calculate multi - plication and addition

$2\times4+2=8 + 2=10$.

Step1: Calculate $a^{2}$ and $b^{2}$

$a^{2}=2^{2}=4$, $b^{2}=4^{2}=16$.

Step2: Calculate the numerator

$a^{2}+b^{2}=4 + 16=20$.

Step3: Calculate the denominator

$a - b=2-4=-2$.

Step4: Calculate the fraction

$\frac{a^{2}+b^{2}}{a - b}=\frac{20}{-2}=-10$.

Answer:

$f(-7)=-29$

2. For the function $g(x)=2x^{2}-x$, find $g(-2)$