If f(a) = 1, find the value of 'a'.

[Alex.Jorgin]

I have this question I'm just wondering how to solve it.

here is the question:

Given: f(x) = x^2 - 6x + 10

if f(a) = 1, what is the value of a?

 

[Dr.Peterson]

here is the question:

Given: f(x) = x^2 - 6x + 10

if f(a) = 1, what is the value of a?

The equation [imath]f(a) = 1[/imath] means [math]a^2-6a+10=1[/math]
So, solve that equation.

If you have trouble doing that, please show us what you have tried, so we can see what sort of help you need:

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[Steven G]

Whenever you are stuck you should look at the definitions. As Dr Peterson pointed out, f(a) = a² - 6a + 10 and is given to equal 1

 

[The Highlander]

I have this question I'm just wondering how to solve it.

here is the question:

Given: f(x) = x^2 - 6x + 10

if f(a) = 1, what is the value of a?

You've been told that The equation [imath]f(a) = 1[/imath] means:-

[math]a^2-6a+10=1[/math]
But that also means that:-
[math]a^2-6a+9=0[/math]
Can you factorise that equation? To get:-

[imath](a\,\pm\,?)(a\,\pm\,?)=0[/imath]
(Replacing each "[imath]\pm\,?[/imath]" with an appropriate value.)​

Do you know what the Discriminant is?
(And what its significance is?)
In this case it is zero; what does that tell you?

Hope that helps.

 

[TristanH]

I have this question I'm just wondering how to solve it.

here is the question:

Given: f(x) = x^2 - 6x + 10

if f(a) = 1, what is the value of a?

First, evaluate
1=a^2 - 6a + 10
1 = (a - 3)^2 + 1
0 = (a - 3)^2
0 = a - 3
3 = a
Next, plug in.
9-18+10=1
So, a is equal to 3

 

[Dr.Peterson]

First, evaluate
1=a^2 - 6a + 10
1 = (a - 3)^2 + 1
0 = (a - 3)^2
0 = a - 3
3 = a
Next, plug in.
9-18+10=1
So, a is equal to 3

Technically, you are not evaluating (which means finding the value of an expression) but solving.

But this is a valid solution by completing the square (maybe the OP is familiar with that method); and you followed that by checking the solution, which is a good practice to demonstrate.

 

[TristanH]

Technically, you are not evaluating (which means finding the value of an expression) but solving.

But this is a valid solution by completing the square (maybe the OP is familiar with that method); and you followed that by checking the solution, which is a good practice to demonstrate.

Ah yes, thank you for sharing my grammar mistake, English is not one of my strong suits.