Answer :
To solve the problem, we need to calculate the expression [tex]\((f - g)(144)\)[/tex] using the functions given:
1. Understand the functions:
- [tex]\( f(x) = \sqrt{x} + 12 \)[/tex]
- [tex]\( g(x) = 2\sqrt{x} \)[/tex]
2. Evaluate each function at [tex]\( x = 144 \)[/tex]:
- For [tex]\( f(x) \)[/tex]:
- Plug in [tex]\( x = 144 \)[/tex]:
[tex]\[ f(144) = \sqrt{144} + 12 \][/tex]
- The square root of 144 is 12, so:
[tex]\[ f(144) = 12 + 12 = 24 \][/tex]
- For [tex]\( g(x) \)[/tex]:
- Plug in [tex]\( x = 144 \)[/tex]:
[tex]\[ g(144) = 2 \times \sqrt{144} \][/tex]
- The square root of 144 is 12, so:
[tex]\[ g(144) = 2 \times 12 = 24 \][/tex]
3. Calculate [tex]\((f - g)(144)\)[/tex]:
- Use the results for [tex]\( f(144) \)[/tex] and [tex]\( g(144) \)[/tex]:
[tex]\[ (f - g)(144) = f(144) - g(144) = 24 - 24 = 0 \][/tex]
Therefore, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\(0\)[/tex].
1. Understand the functions:
- [tex]\( f(x) = \sqrt{x} + 12 \)[/tex]
- [tex]\( g(x) = 2\sqrt{x} \)[/tex]
2. Evaluate each function at [tex]\( x = 144 \)[/tex]:
- For [tex]\( f(x) \)[/tex]:
- Plug in [tex]\( x = 144 \)[/tex]:
[tex]\[ f(144) = \sqrt{144} + 12 \][/tex]
- The square root of 144 is 12, so:
[tex]\[ f(144) = 12 + 12 = 24 \][/tex]
- For [tex]\( g(x) \)[/tex]:
- Plug in [tex]\( x = 144 \)[/tex]:
[tex]\[ g(144) = 2 \times \sqrt{144} \][/tex]
- The square root of 144 is 12, so:
[tex]\[ g(144) = 2 \times 12 = 24 \][/tex]
3. Calculate [tex]\((f - g)(144)\)[/tex]:
- Use the results for [tex]\( f(144) \)[/tex] and [tex]\( g(144) \)[/tex]:
[tex]\[ (f - g)(144) = f(144) - g(144) = 24 - 24 = 0 \][/tex]
Therefore, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\(0\)[/tex].
