Hi, I just joined cuz I need help with this problem.... thank you :* Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. ->f(x)=(x+a)/b ->g(x)=cx−d -Show your work to prove that the inverse of f(x) is g(x). - Show your work to evaluate g(f(x)). - Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

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Hi, I just joined cuz I need help with this problem.... thank you :* Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses. ->f(x)=(x+a)/b ->g(x)=cx−d -Show your work to prove that the inverse of f(x) is g(x). - Show your work to evaluate g(f(x)). - Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

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In the 1st equation write $$ y=\frac{x+a}{b} $$ Then replace x with y and y with x: $$ x=\frac{y+a}{b} $$ Then, solve for y. This is the inverse of \(f(x)\) You will immediately see what \(c\) and \(d\) should be.
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What numbers should I use?

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lol thanks @GretaKnows
I'm using a=5 and b=3.... that's ok right?
Did you check that the function you got was the inverse of the other
This is what i got soo far for part 1 and part 2... I'm not sure if its correct Part 1: f(x) = x + 5/3 (g(x) = (x+5)/3 Part 2: f(x) = 3x -5 Change f(x) for y: y = 3x -5 Switch the x and y: x =3y -5 Isolate the y by adding five to both sides: x + 5 =3y Divide both sides by 3: x+5=3y / 3 y=x+5/ 3 That’s how you get: y = x+5 / 3
When you graph f(x) and g(x) just choose 5 points for each and graph. Say x=-3, -2, 0, 1, 2 Then graph y=x. You should see that f(x) is a mirror image of g(x) about the line y=x
Wait...... is part 1 and part 2 correct?????
But is it correct or not???
In your Part 1 Given \(a=5\) and \(b=3\) $$ f(x)=\frac{x+5}{3} $$ Not $$ f(x)=x+5/3 $$ Based on your original function. Be careful when dividing quantities, here we are dividing the entire quantity x+5 b 3, not just dividing 5 by 3. Make sense? In Part 2, your process is good, just remember the division issue I just mentioned. Redo it with this in mind.
so i changed it to this..... f(x) = (x+5)/3????
yes and then redo your work using that equation for f(x)

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