some kind of crazy math i dont know how to do, help!!!!?

Question

Let f(x)=3x-1 and g(x)=x-2
(a) If 2f(a)-3g(a)=5，find the value of a
(b) If f(2b)-g(3b)=5，find the value of b

Answer 1

just substitute 3a-1 for f(a) and x-2 for g(a):

2(3a-1) - 3(a-2) = 5
6a - 2 - 3a + 6 = 5
3a + 4 = 5
3a = 1
a = 1/3

you do the next one ...

Answer 2

Its very simple.
Solution for (a)

2f(a)-3g(a)=5

now replace values of f(a)= 3a-1 and g(a)=a-2
=> 2(3a-1) -3 (a-2) = 5
=>6a-2 -3a +6 = 5
=>3a + 4 = 5
=> 3a = 1
=>a = 1/3

solution (b)

f(2b) - g(3b) = 5

replace original values of x in f(x) & g(x) with 2b & 3b respectively. And we get,

=>[3(2b)-1] - [3b-2] = 5
=>6b -1 - 3b +2 = 5
=> 3b + 1 = 5
=> 3b = 4
=>b = 4/3

Hey, let me know if this answers were correct.

Answer 3

This is functional notation. When you have something like f(x)=3x-1, that's just a mathematical way of saying taking x, multiply it by 3, subtract one and the result is called f(x). If x is a particular real number, then you can calculate f(x) for that number.

Let me walk you through how to do these problems.

(a) 2f(a)-3g(a)=5

using f(x) and g(x) as defined means

f(a) = 3a-1 and g(a) = a-2

so the equation becomes

2(3a-1)-3(a-2) = 5
6a-2-3a+6=5
3a=1
a=1/3

(b) f(2b) = 3(2b)-1 = 6b-1
g(3b) = 3b-2

f(2b)-g(3b)=5

6b-1-(3b-2)=5
6b-1-3b+2=5
3b=4
b=4/3

Hope that helps you see how to do these!

Answer 4

Let f(x)=3x-1 and g(x)=x-2
(a) If 2f(a)-3g(a)=5，find the value of a
2*(3a-1)-3*(a-2)=5
6a-2-3a+6=5
3a+4=5
3a=1
a=1/3

f(x)=3x-1 and g(x)=x-2
(b) If f(2b)-g(3b)=5，find the value of b
(3*2b-1)-(3b-2)=5
6b-1-3b+2=5
3b+1=5
3b=4
b=4/3

Answer 5

QUESTION

Let f(x)=3x-1 and g(x)=x-2
(a) If 2f(a)-3g(a)=5，find the value of a
(b) If f(2b)-g(3b)=5，find the value of b

SOLUTION
f(x)=3x-1 therefore f(a)=3a-1 2f(a) = 6a-2
g(x)=x-2 therefore g(a) = a-2 3g(a) = 3a-6

Given 2f(a)-3g(a)=5;
6a-2-(3a-6)=5 Expanding 6a-2-3a+6= 5
Hence 3a=1
a= 1/3

f(x)=3x-1 therefore f(2b)= 6b-1 in place of x substitute 2b
g(x)=x-2 therefor g(3b) = 3b-2 In place of substitute 3b

Given
f(2b)-g(3b)=5 Hence 6b-1 -(3b-2)=5
6b-1-3b+2=4
6b-3b=4+1-2
3b=3
b=1

Answer 6

for me the equations are....

(a) solve for a...

2(3a-1)-3(a-2)= 5
6a-2-3a+6=5
6a-3a+4=5
3a=5-4
3a=1
a=1/3

(b)solve for b...

2(3b-1)-3(b-2)=5
6b-2-3b+6=5
3b+4=5
3b=5-4
3b=1
b=1/3

that's all... very simple

Answer 7

Just replace what is inside the f(), for the x variable of it.

For example:

a) 2 * f(a) - 3 * g(a) = 5

2 * f(3a-1) - 3 * g(a-2) = 5

2(3a-1) - 3(a-2) = 5
6a-2 -3a+2 = 5
3a = 5
a = 5/3

Answer 8

Just plug and chug..
put a into f(x) and g(x)
put those expressions into the big equation:
2(3a-1)-3(a-2) = 5
Now just collect terms and solve for a

Same thing on b, sort of. a little trickier though

Answer 9

Is this homework from Crazy Math 101 ?