+389 (a)\(Suppose the domain of $f$ is $(-1,1)$. Define the function $g$ by $$g(x)=f(x+1).$$ What is the domain of $g$?\)(b)\(Suppose the domain of $f$ is $(-1,1)$. Define the function $h$ by $$h(x)=f(x)+1.$$ What is the domain of $h$?\)(c)
\(Suppose the domain of $f$ is $(-1,1)$. Define the function $j$ by $$j(x)=f(1/x).$$ What is the domain of $j$? \)(d)
\(Suppose the domain of $f$ is $(-1,1)$. Define the function $k$ by $$k(x)=f\left(\sqrt x\right).$$ What is the domain of $k$?\)(e)\(Suppose the domain of $f$ is $(-1,1)$. Define the function $\ell$ by $$\ell(x)=f\left(\frac{x+1}{x-1}\right).$$ What is the domain of $\ell$?\)
+33661 I'll rewrite the question:
Suppose the domain of f is (-1, 1)
a) Define the function g by g(x) = f(x+1) What is the domain of g?
b) Define the function h by h(x) = f(x) + 1 What is the domain of h?
c) Define the function j by j(x) = f(1/x) What is the domain of j?
d) Define the function k by k(x) = f(sqrt(x)) What is the domain of k?
e) Define the function L by L(x) = f( (x+1)/(x-1) ) What is the domain of L?
and I'll answer the first one:
a) Minimum value of domain of f is -1, so xmin + 1 = -1, or xmin = -2
Maximum value of domain of f is +1 so xmax + 1 = 1, or xmax = 0
Hence domain of g is (-2, 0)
Now you try some of the others.
