Algebra 1 Help ?

Question

Algebra 1 Help ?

andrewthecookie · Answer

yes man in a cowboy i shall halp u

conqueror · Answer

Part 1. 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.

$$f(x) = x + a \div b$$
$$g(x) = cx - d$$

dantefemboy · Answer

Sure.

conqueror · Answer

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conqueror · Answer

@hartnn

conqueror · Answer

:/

conqueror · Answer

@campbell_st

conqueror · Answer

Do you know any of this ? o.o

campbell_st · Answer

ok... so let  a = -1 and b = 2

$$f(x) = \frac{x -1}{2}$$

then the rest is a bit odd as I would have thought 

g(x) = bx - a    would have been the inverse

so 

g(x) = 2x + 1


so go back to 

$$f(x) = \frac{x - 1}{2}$$

rewrite it as 

$$y = \frac{x - 1}{2}$$

to find the inverse swap x and y

$$x = \frac{y - 1}{2}$$

now make y the subject and see if you come up with g(x) above.

hope it makes sense

conqueror · Answer

Would g(x) be:

x = 2y + 1 ?

conqueror · Answer

@campbell_st

campbell_st · Answer

just check if you have 

$$x = \frac{y - 1}{2}$$

so making y the subject of this equation...

would result in ..?

conqueror · Answer

What do you mean subject of the equation ?

campbell_st · Answer

isolate y... or get it on it's own so its 

y = something in terms of x

conqueror · Answer

x2 + 1 ?

campbell_st · Answer

close

y = 2x + 1

so is this g(x) ...? if you go back and look at what I said about g(x) in the initial post

conqueror · Answer

Ohhh, so y would just replace g(x) ?

campbell_st · Answer

that's correct.... the process of finding an inverse is

write it as 

y = ax + b

swap x and y

then make y the subject... 

so you started with 

$$f(x) = \frac{x - 1}{2}$$

and showed the inverse was 

$$g(x) = 2x + 1$$

hope it all made sense

conqueror · Answer

Part 3. Show your work to evaluate g(f(x)).

Part 4. 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.

conqueror · Answer

@campbell_st

campbell_st · Answer

so in g(x) = 2x + 1 

replace x with $$\frac{x -1}{2}$$

then simplify it

conqueror · Answer

What do you mean ? So I replace the x's in the function with x - 1 / 2 ?

campbell_st · Answer

$$g(x) = 2x + 1 ~~~then~~~~g(f(x)) = 2(\frac{x -1}{2}) + 1$$

simplify this

conqueror · Answer

Simplify g(f(x))=2(x−12)+1 ?

conqueror · Answer

Sorry if it looks wrong, I just copied and pasted your equation form.

conqueror · Answer

?

campbell_st · Answer

so can you simplify 

$$g(f(x) = 2 \times \frac{x -1}{2} + 1$$

campbell_st · Answer

you only need to simplify the right hand side

conqueror · Answer

Am I supposed to graph that ? @campbell_st

conqueror · Answer

@campbell_st