Question

1.Determine if f is one to one for \\(f(x)=x^{2} – 5x+1)\\ when x = 0
a.almost
b.none of the option
c.yes
d.No

2.Let \\(f(x)=x^{2}-4x +7)\\, find \\(\\frac{f(x+\\Delta x)-f(x)}{\\Delta x})\\
a.\\(2x-\\Delta x+4)\\
b.\\(2x+\\Delta x+4)\\
c.\\(2x-\\Delta x-4)\\
d.\\(2x+\\Delta x-4)\\

Answer 1

1) d

let's solve the equation f(x)=0

$x^2-5x+1=0$

$x=\frac{5\pm\sqrt{21}}{2}$

This equation has two roots, therefore this function is not one-to-one

2) d

$f(x+\Delta x)-f(x)=(x+\Delta x)^2-4(x+\Delta x)+7-x^2+4x-7=x^2+2x\Delta x+\Delta^2-4(x+\Delta x)-x^2+4x=$

$=2x\Delta x+\Delta^2x-4\Delta x$

$\frac{}{}$ $\frac{f(x+\Delta x)-f(x)}{\Delta x}=\frac{2x\Delta x+\Delta^2x-4\Delta x}{\Delta x}=2x+\Delta x-4$