The expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]
The function is given as:
[tex]f(x) = \sqrt{x[/tex]
When the function is stretched horizontally by a factor of 2, the rule is:
f'(x) = f(x/2)
So, we have:
[tex]f'(x) = \sqrt{\frac x2[/tex]
When the function is shifted left by 1 unit, the rule is:
f"(x) = f(x + 1)
So, we have:
[tex]f"'(x) = \sqrt{\frac {x - 1}2[/tex]
When the function is shifted up by 3 units, the rule is:
g(x) = f"(x) + 3
So, we have:
[tex]g(x) = \sqrt{\frac {x - 1}2} + 3[/tex]
Hence, the expression of function g(x) is [tex]\sqrt{\frac {x - 1}2} + 3[/tex]
Read more about function transformation at:
https://brainly.com/question/13810353
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