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Question
Hello -- I'm having some difficulty understanding and simplifying (algebraically) the following:
g(x)= 3f(x+1)-2
Can you explain this to me/ thanks .. Angelo

Answer
Angelo,
f(x), g(x) etc are functions of the variables given in the brackets.
Let us take a simpler example: f(x) = x + 2
So f(2) = 2+2 =4.

Now you have been given g(x)= 3f(x+1)-2. This means that g(x) is a function of f(x+1). For this to solve, we need to know f(x) which is not given in your example. Let us assume f(x) = x+2.
Considering this,
f(x+1 = (x+1)+2 . Note that we have replaces x with x+2 here as this is a function of x+1 and not x.
Thus, f(x+1) = x+3
We will substitute this in g(x)
Thus,
g(x) = 3[x+3]-2 = 3x+9-2 = 3x+7
So if you are asked to find g(4), then it will equal to 3(4)+7 = 19

You can find g(x) for any x provided you know the equation for f(x).
I hope that this is clear. Please let me know if you need additional information.
All the best.

Regards,
Pawan

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Pawan Musale

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I can answer Basic Mathematics questions like: Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc I can try to answer questions of probability and set theory

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Tutoring on allexperts.com since long time

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I am Bachelor of Engineering (Instrumentation) from the reputed institute in India.

Awards and Honors
I was 18th in High School Scholarship examination in Maharashtra State of India. I was second in Mathematics in Maharashtra State in Secondary School Certificate examination.

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