Let g the inverse function of f.
The most important property of g and f being inverses of each other, is that
g(f(x))=x, also f(g(x))=x
so, what one function 'does' to x, the other 'undoes' it.
Thus, we have:
f(g(x))=x and alos f(g(x))= -g(x)+3, from the rule
thus :
-g(x)+3=x
-g(x)=x-3
g(x)=-x+3
check: f(g(x))=f(-x+3)=-(-x+3)+3=x-3+3=x
Answer: the inverse of f is g, such that g(x)=-x+3
Answer:
<h2>L=203 yards</h2><h2>W=52 yards</h2>
Step-by-step explanation:
Step one:
given data
perimeter= 510 yards
let the width be x, width=x
length= (4x-5)-----quadruple mean 4 times
Step two:
the expression for perimeter is
P=2L+2W
510=2(4x-5)+2x
510=8x-10+2x
510+10=8x+2x
520=10x
divide both sides by 10
x=520/10
x=52
the width is 52 yards
the lenght is (4x-5)
L=4(52)-5
L=208-5
L=203 yards
The question is telling you that the length of the rectangle is 3 metres more than twice the width.
So let:
<em>w= width</em>
<em>L= length</em>
Because the length is 3 metres more than twice<em> </em>the width: <em>L= </em><em>2</em><em>w+</em><em>3</em>
They also tell you the perimeter is 48 metres.
<em>P= L+L+w+w</em>
So the equation of the perimeter is:
<em>48= (2w+3)+(2w+3)+2w +2w</em>
<em>48= 2(2w+3) + 4w</em>
To find w, expand and simplify.
<em>48= 4w+6+4w</em>
<em>48= 8w + 6</em>
<em>42= 8w</em>
<em>5.25=w</em>
Now that you know the width, plug in the value into the length equation:
<em>L= 2w+3</em>
<em>L=2(5.25)+3</em>
<em>L=10.50+3</em>
<em>L=13.5</em>
If I am wrong let me know! I hope this helps.
Since the denominators are the same, just subtract the numerators.
The answer is 3/10.
