Help please
to solve f(a+1) you need to substitute (a+1) for every value of x:
f(a + 1) = 3(a+1)^2 - (a+1) + 4
Now expand and simplify:
f(a + 1) = 3(a^2 + 2a + 1) - a - 1 + 4
= 3a^2 + 6a + 3 - a + 3
= 3a^2 -7a + 6
There you go :)
For the second one, you simply need to substitute a for x and multiply the entire equation by 2:
[f(a)]2 = 2(3a^2 - a + 4)
= 6a^2 - 2a + 8
If the question was to let these equations equal each other to find a, then do this:
3a^2 - 7a + 6 = 6a^2 - 2a + 8
Now take 3a^2 from both sides:
-7a + 6 = 3a^2 - 2a + 8
Now add 7a to both sides:
6 = 3a^2 + 5a + 8
Now take 6 from both sides:
0 = 3a^2 + 5a + 2
Now factorise:
(3a + 2)(a + 1) = 0
Now using the factor law you can solve:
3a + 2 = 0 OR a + 1 = 0
3a = -2 OR a = -1
a = -2/3 OR a = -1
Hope this helps :)
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Verified answer
to solve f(a+1) you need to substitute (a+1) for every value of x:
f(a + 1) = 3(a+1)^2 - (a+1) + 4
Now expand and simplify:
f(a + 1) = 3(a^2 + 2a + 1) - a - 1 + 4
= 3a^2 + 6a + 3 - a + 3
= 3a^2 -7a + 6
There you go :)
For the second one, you simply need to substitute a for x and multiply the entire equation by 2:
[f(a)]2 = 2(3a^2 - a + 4)
= 6a^2 - 2a + 8
If the question was to let these equations equal each other to find a, then do this:
3a^2 - 7a + 6 = 6a^2 - 2a + 8
Now take 3a^2 from both sides:
-7a + 6 = 3a^2 - 2a + 8
Now add 7a to both sides:
6 = 3a^2 + 5a + 8
Now take 6 from both sides:
0 = 3a^2 + 5a + 2
Now factorise:
(3a + 2)(a + 1) = 0
Now using the factor law you can solve:
3a + 2 = 0 OR a + 1 = 0
3a = -2 OR a = -1
a = -2/3 OR a = -1
There you go :)
Hope this helps :)