Some Basic Calc. Questions

[abelkhouche]

Hi everyone,

I'm new to the forum. I'm taking a calculus class in college after having not taken a math class in quite a while. Some things seem familiar, others more difficult. I was having problems with a couple problems I was given. I will show my work where it applies and I appreciate any help given in advance.

This is the first problem.

Suppose f is a function that satisfies the relation f(2x-4)=x+7

a. What value of x should you plug into the relation in order to determine f(6)

So I understand (at least I think) that in this question we want for:
2x-4=6
x=5 (Correct me if I'm wrong)

The next question
b. Using the value of x found in part (a), determine the value of f(6)

Are we inputting 5 into the right side of the equation so that in this case:
f(6)=5+7
f(6)=12 (Let me know if I'm wrong

The last question is the one I'm having the most trouble with:

c. Find a formula for f(t) in general.

I have no idea what this question is asking, where are we supposed to plug the value t?


Thanks in advance to anyone who took the time help me out!

 

[Deleted member 4993]

Hi everyone,

I'm new to the forum. I'm taking a calculus class in college after having not taken a math class in quite a while. Some things seem familiar, others more difficult. I was having problems with a couple problems I was given. I will show my work where it applies and I appreciate any help given in advance.

This is the first problem.

Suppose f is a function that satisfies the relation f(2x-4)=x+7

a. What value of x should you plug into the relation in order to determine f(6)

So I understand (at least I think) that in this question we want for:
2x-4=6
x=5 (Correct me if I'm wrong) .......... Correct

The next question
b. Using the value of x found in part (a), determine the value of f(6)

Are we inputting 5 into the right side of the equation so that in this case:
f(6)=5+7
f(6)=12 (Let me know if I'm wrong .......... Correct

The last question is the one I'm having the most trouble with:

c. Find a formula for f(t) in general.

I have no idea what this question is asking, where are we supposed to plug the value t?


Thanks in advance to anyone who took the time help me out!

Hint:

f(2x-4) = 1/2*(2x -4) + 9

 

[abelkhouche]

Hint:

f(2x-4) = 1/2*(2x -4) + 9

I appreciate the help Subhotosh, I think I got it now.

 

[Otis]

f(2x-4)=x+7

Find a formula for f(t) in general.

... where are we supposed to plug the value t?

We're told that, if we input the value 2x-4 into function f, the value x+7 comes out.

Now they want you to express the input using symbol t, instead, for the same function. In other words,

Let t = 2x-4

To find the corresponding output of function f, when the input is t, you can solve the equation above for x, and then substitute the result for x in the original formula for f (quoted in blue, above).